On cosmological mass with positive Λ

For asymptotically flat space-times, a very satisfactory expression for the total mass/energy of a system defined at future null infinity was provided by Bondi and Sachs, in the early 1960s. A generalization of this to space-times that are asymptotically de Sitter now has particular relevance in view of observational evidence, from 1998 onwards, indicating the presence of a positive cosmological constant Lambda. In this article, some of the issues involved in such a definition are examined, showing that a somewhat different attitude to mass/energy must be taken, from that which was appropriate for asymptotically flat space-times. Two tentative suggestions are put forward for a retarded mass/energy definition with positive Lambda, one based on a conformally invariant integral expression whose advanced time-derivative gives the Bondi-Sachs definition in the asymptotically flat case and the other, on the author's 1982 approach to quasi-local energy. Such expressions could have some direct relevance to the proposal of Conformal Cyclic Cosmology, for which recent analysis of the CMB has provided some striking support.